What is a confusion matrix in simple terms?

A 2×2 table (for binary classification) that sorts every prediction into four boxes: true positives, false positives, false negatives and true negatives. All the common classification metrics — accuracy, precision, recall, F1 — are computed from those four counts.

What is the difference between a false positive and a false negative?

A false positive is a negative case the model wrongly flagged as positive (a healthy patient flagged as sick). A false negative is a positive case the model missed (a sick patient cleared as healthy). Which error is worse depends entirely on the application.

Why is accuracy a bad metric for imbalanced data?

Because predicting the majority class for everything can score very high accuracy while catching none of the rare class. With 1% fraud, an always-'not-fraud' model is 99% accurate and 0% useful — precision and recall expose this immediately.

How does a confusion matrix work with more than two classes?

It becomes an N×N table: rows are predicted classes, columns are actual classes, and the diagonal holds correct predictions. Per-class precision and recall are computed by treating each class as 'positive' against all the rest.

GuideJuly 15, 2026Learn AI & Data Science

Confusion Matrix Explained: TP, FP, FN, TN — and the Metrics They Build

What a confusion matrix is, how to read true/false positives and negatives, and how accuracy, precision, recall and F1 are computed from its four cells.

A confusion matrix is the single most useful table in classification. It takes every prediction your model made and sorts it into one of four boxes: the model said *yes* and was right, said *yes* and was wrong, said *no* and was wrong, or said *no* and was right. Once you can read those four boxes, every headline metric — accuracy, precision, recall, F1 — stops being a formula to memorise and becomes something you can see.

The four cells

	Actually positive	Actually negative
Predicted positive	True positive (TP)	False positive (FP)
Predicted negative	False negative (FN)	True negative (TN)

The naming convention trips people up less once you split each term in two: the second word (*positive/negative*) is what the model predicted, and the first word (*true/false*) says whether that prediction was correct. So a *false negative* is a case the model called negative — falsely. In a disease screening, that's a sick patient sent home; in spam filtering, it's a spam email that reached the inbox.

The metrics the matrix builds

Accuracy = (TP + TN) / all predictions — the fraction the model got right overall.
Precision = TP / (TP + FP) — of everything flagged positive, how much really was.
Recall (sensitivity) = TP / (TP + FN) — of all real positives, how many were caught.
Specificity = TN / (TN + FP) — of all real negatives, how many were correctly cleared.
F1 score = the harmonic mean of precision and recall — a single number that punishes a big gap between them.

Why accuracy alone misleads

Imagine a fraud dataset where 1 in 100 transactions is fraudulent. A model that predicts 'not fraud' for everything scores 99% accuracy while catching zero fraud — its confusion matrix has an empty TP cell. This is the class-imbalance trap, and it's exactly why practitioners read the matrix before the headline number. Precision and recall stay honest because they focus on the rare class; accuracy averages the problem away.

Read the matrix before any metric

When a model 'scores well', glance at the raw four cells first. An empty or tiny TP cell, or an FP count dwarfing TP, tells you more in two seconds than any single summary number.

From the matrix to curves

Most classifiers output a probability, and the confusion matrix you get depends on where you set the decision threshold. Sweep that threshold from 0 to 1 and you trace out the ROC and precision–recall curves — the natural next step once the matrix makes sense. We cover those in our ROC and precision–recall curves topic page, and the matrix itself in more drill-style depth in confusion matrix and precision/recall.

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